An aerostatic bearing includes a slider that is guidable on a guide surface. The slider has an inner, conical sliding surface of an inner air bearing facing the guide surface with a central compressed air supply. The conical sliding surface is attached by first joints to the central compressed air supply and by second joints to a base of the slider arranged on a side of the slider facing away from the guide surface, such that a cone angle of the conical sliding surface is variable. The conical sliding surface is surrounded by an annular sliding surface of an outer air bearing having an annular compressed air supply.